Smooth associative operations on finite ordinal scales

IEEE Transactions on Fuzzy Systems

Volumn 8, Issue 6, 2000, Pages 791-795

  Fodor, János ^a  

^a SZENT ISTVÁN UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EQUIVALENCE CLASSES; MATHEMATICAL MODELS; NUMBER THEORY; THEOREM PROVING;

FINITE ORDINAL SCALES; INTERMEDIATE VALUE THEOREM; SMOOTH ASSOCIATIVE OPERATIONS;

FUZZY SETS;

EID: 0034476660     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/91.890343     Document Type: Article

References (16)

1. T. Calvo, B. De Baets, and J. C. Fodor, "The functional equations of Frank and Alsina for uninorms and nullnorms," Fuzzy Sets Syst., to be published.
2. B. De Baets and R. Mesiar, "Discrete triangular norms," in Topological and Algebraic Structures, E. P. Klement and S. E. Rodabaugh, Eds. Linz, Austria: Johannes Kepler Universität Linz, 1999, pp. 6-8.
3. J. C. Fodor, "An extension of Fung-Fu's theorem," Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst., vol. 4, pp. 235-243, 1996.
4. J. Fodor and T. Calvo, "Aggregation functions defined by t-norms and t-conorms," in Aggregation and Fusion of Imperfect Information, B. Bouchon-Meunier, Ed. New York: Physica-Verlag, 1998, pp. 36-48.
5. L. Fuchs, Partially Ordered Algebraic Systems. Reading, MA: Addison-Wesley, 1963.
6. L. W. Fung and K. S. Fu et al., "An axiomatic approach to rational decision making in a fuzzy environment," in Fuzzy Sets and Their Applications to Cognitive and Decision Processes, L. A. Zadeh et al., Eds. New York: Academic, 1975, pp. 227-256.
7. L. Godo and C. Sierra, "A new approach to connective generation in the framework of expert systems using fuzzy logic," in Proc. 18th Int. Symp. Multiple-Valued Logic, Washington, DC, 1988, pp. 157-162.
8. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norms, Dordrecht, The Netherlands: Kluwer, 2000.
9. M. Komornikova, "Smoothly generated discrete aggregation operators," BUSEFAL, vol. 80, 1999.
10. J.-L. Marichal, "On the associativity functional equation," Univ. Liěge, Liège, Belgium, Working Papers GEMME no. 9805, Jan. 1998.
11. M. Mas, G. Mayor, and J. Torrens, "t-operators and uninorms on a finite totally ordered set," Int. J. Intell. Syst., vol. 14, 1999.
12. M. Mas, J. Torrens, T. Calvo, and M. Carbonell, "Idempotent operators on a finite chain," Mathware Soft Computing, vol. 6, pp. 235-247, 1999.
13. G. Mayor and J. Torrens, "On a class of operators for expert systems," Int. J. Intell. Syst., vol. 8, pp. 771-778, 1993.
14. F. S. Roberts, Measurement Theory. Reading, MA: Addison-Wesley, 1978, vol. 7. Encyclopedia Mathematics Applications.
15. W. Sander, "Associativity," in Proc. Numbers, Functions, Equations '98 Int. Conf. - Leaflets in Mathematics. Pécs, Hyngary, 1998, pp. 139-140.
16. R. R. Yager, "Non-numeric multi-criteria multi-person decision making," Group Decisions Negotiation, vol. 2, pp. 81-93, 1993.